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Lixin Xu

Lixin Xu contributes to research discovery and scholarly infrastructure.

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astro-ph.CO Computer Vision Graphics hep-th Machine Learning math-ph math.MP

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preprint2026arXiv

Equivariant Cohomology, BRST Quantization, and Analytic Localization: A Unified Framework

This paper provides a detailed exposition of the two main models for equivariant cohomology -- the Cartan and Weil models -- and their explicit isomorphism via the Kalkman (Mathai--Quillen) transformation. We then connect this framework to the BRST quantization of gauge theories, showing how the BRST complex can be identified with the Cartan model. Viewing both the Kalkman transformation and Witten's Morse-theoretic deformation as gauge-fixing procedures leads naturally to the \emph{equivariant Witten deformation}. This combined perspective yields a transparent analytic proof of the Atiyah--Bott--Berline--Vergne (ABBV) localization formula for integrals of equivariantly closed forms.The theory is richly illustrated with computations on $\mathbb{CP}^1$ and $\mathbb{CP}^n$, supplemented by explicit coordinate calculations.

preprint2026arXiv

R-DMesh: Video-Guided 3D Animation via Rectified Dynamic Mesh Flow

Video-guided 3D animation holds immense potential for content creation, offering intuitive and precise control over dynamic assets. However, practical deployment faces a critical yet frequently overlooked hurdle: the pose misalignment dilemma. In real-world scenarios, the initial pose of a user-provided static mesh rarely aligns with the starting frame of a reference video. Naively forcing a mesh to follow a mismatched trajectory inevitably leads to severe geometric distortion or animation failure. To address this, we present Rectified Dynamic Mesh (R-DMesh), a unified framework designed to generate high-fidelity 4D meshes that are ``rectified'' to align with video context. Unlike standard motion transfer approaches, our method introduces a novel VAE that explicitly disentangles the input into a conditional base mesh, relative motion trajectories, and a crucial rectification jump offset. This offset is learned to automatically transform the arbitrary pose of the input mesh to match the video's initial state before animation begins. We process these components via a Triflow Attention mechanism, which leverages vertex-wise geometric features to modulate the three orthogonal flows, ensuring physical consistency and local rigidity during the rectification and animation process. For generation, we employ a Rectified Flow-based Diffusion Transformer conditioned on pre-trained video latents, effectively transferring rich spatio-temporal priors to the 3D domain. To support this task, we construct Video-RDMesh, a large-scale dataset of over 500k dynamic mesh sequences specifically curated to simulate pose misalignment. Extensive experiments demonstrate that R-DMesh not only solves the alignment problem but also enables robust downstream applications, including pose retargeting and holistic 4D generation.

preprint2022arXiv

Can phantom transition at $z\sim 1$ restore the Cosmic concordance?

The tension among inferences of Hubble constant ($H_0$) is found in a large array of datasets combinations. Modification to the late expansion history is the most direct solution to this discrepancy. In this work, we examine the viability of restoring the cosmological concordance with a novel version of transitional dark energy (TDE). The main anchors for the cosmic distance scale: cosmic microwave background (CMB) radiation, baryon acoustic oscillation (BAO), and Type Ia supernova (SNe Ia) calibrated by Cepheids form a "impossible trinity", i.e., it's plausible to reconcile with any two of the three but unlikely to accommodate them all. Particularly, the tension between BAO and the calibrated SNe Ia can not be reconciled within the scenarios of late dark energy. Nevertheless, our analysis suggests that the TDE model can reconcile with CMB and SNe Ia calibrated by its absolute magnitude ($M_{\rm{B}}$) when the equation of state (EoS) of DE transits around $z\sim1$. Meanwhile, we see a positive sign that the EoS transits with the inclusion of a local prior on $M_{\rm{B}}$, whereas the opposite is true without the $M_{\rm{B}}$ prior.

preprint2022arXiv

Comparing the scalar-field dark energy models with recent observations

We investigate the general properties of a class of scalar-field dark energy models (i.e., $ϕ$CDM models) which behave like cosmological trackers at early times. Particularly, we choose three $ϕ$CDM models with typical potentials, i.e., $V(ϕ)\propto ϕ^{-α}$ (inverse power-law (IPL) model), $V(ϕ)\propto \coth^αϕ$ (L-model) and $V(ϕ)\propto \cosh(αϕ)$ (Oscillatory tracker model), where the latter two models are based on the $α$-attractors originated from the study of inflation. These models, which reduce to the $Λ$CDM model with $α\to 0$, are studied and compared with the recent observations, including the Pantheon sample of type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, BOSS and eBOSS, as well as the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from Planck 2018 results. The observational constraints from the combining sample (SNe Ia + BAO + CMB) indicate that none of the three $ϕ$CDM models exclude the $Λ$CDM model at $68.3\%$ confidence level. We find that the CMB anisotropy data have obvious advantages in constraining the dark energy models compared with other cosmological probes, which is particularly evident in the L-model. Furthermore, we apply the Bayesian evidence to compare the $ϕ$CDM models and the $Λ$CDM model with the analysis of the combining sample. The concordance $Λ$CDM model is still the most supported one. In addition, among the three $ϕ$CDM models, the IPL model is the most competitive one, while the L-model/Oscillatory tacker model is moderately/strongly disfavored.

preprint2022arXiv

Limit on the dark matter mass from its interaction with photons

In this work, we explore the phenomenology of generalized dark matter (GDM) which interacts with photons ($γ$). We assume that DM establishes elastic scattering with $γ$ when it has already become nonrelativistic, otherwise the abundance of DM today is disfavored by current observations. Within this scenario, the equation of state (EoS) of DM is determined by its mass ($m_χ$) and the DM-$γ$ scattering cross-section. The distinctive imprints of a nonzero EoS of DM on CMB angular power spectrum allow us to set a lower limit on $m_χ$ with Planck 2018 data alone, i.e., $m_χ > 8.7$ keV at $95\%$ C.L. In the study of cosmic concordance problems, we find that the GDM scenario preserves the sound horizon ($r_s(z_*)$) predicted in the fiducial $Λ$CDM model, and thus does not solve the $H_0$ tension. When performing the joint analysis of Planck+LSS datasets, the best-fit $S_8= 0.785\pm 0.017$ closely matches the given $S_8$ prior. This suggests that the GDM scenario can be counted as a viable candidate to restore the $S_8$ ($σ_{8}$) tension.

preprint2021arXiv

Testing the effect of $H_0$ on $fσ_8$ tension using a Gaussian Process method

Using the $fσ_8(z)$ redshift space distortion (RSD) data, the $σ_8^0-Ω_m^0$ tension is studied utilizing a parameterization of growth rate $f(z) = Ω_m(z)^γ$. Here, $f(z)$ is derived from the expansion history $H(z)$ which is reconstructed from the observational Hubble data applying the Gaussian Process method. It is found that different priors of $H_0$ have great influences on the evolution curve of $H(z)$ and the constraint of $σ_8^0-Ω_m^0$. When using a larger $H_0$ prior, the low redshifts $H(z)$ deviate significantly from that of the $Λ$CDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the $H_0$ tension problem. The tension between our best-fit values of $σ_8^0-Ω_m^0$ and that of the \textit{Planck} 2018 $Λ$CDM (PLA) will disappear (less than $1σ$) when taking a prior for $H_0$ obtained from PLA. Moreover, the tension exceeds $2σ$ level when applying the prior $H_0 = 73.52 \pm 1.62$ km/s/Mpc resulted from the Hubble Space Telescope photometry. By comparing the $S_8 -Ω_m^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.

preprint2019arXiv

General Cosmography Model with Spatial Curvature

The cosmographic approach is adopted to determine the spatial curvature (i.e., $Ω_K$) combining the latest released cosmic chronometers data (CC), the Pantheon sample of type Ia supernovae observations, and the baryon acoustic oscillation measurements. We use the expanded transverse comoving distance $D_M(z)$ as a basic function for deriving $H(z)$ and the other cosmic distances. In this scenario, $Ω_K$ can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Padé approximants and the Taylor series in terms of the new redshift $y=z/(1+z)$. Adopting the Bayesian evidence, we find that there is positive evidence for the Padé approximant up to order ($2,2$) and weak evidence for the Taylor series up to 3-rd order against $Λ\text{CDM}+Ω_K$ model. The constraint results show that a closed universe is preferred by the present observations under all the approximants used in this study. And the tension level of the Hubble constant $H_0$ is less than $2σ$ significance between different approximants and the local distance ladder determination. For each assumed approximant, $H_0$ is anti-correlated with $Ω_K$ and the sound horizon at the end of the radiation drag epoch, which indicates that the $H_0$ tension problem can be slightly relaxed by introducing $Ω_K$ or any new physics which can reduce the sound horizon in the early universe.

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